Abstract
We examine the accuracy of the microcanonical Lanczos method (MCLM) developed by
Long, {\it et al.} [Phys. Rev. B {\bf 68}, 235106 (2003)]
to compute dynamical spectral functions of
interacting quantum models at finite temperatures.
The MCLM is based on the microcanonical ensemble, which becomes exact in the thermodynamic limit.
To apply the microcanonical ensemble at a fixed temperature, one has to find energy eigenstates with the energy eigenvalue
corresponding to the internal energy in the canonical ensemble.
Here, we propose to use thermal pure quantum state methods by
Sugiura and Shimizu [Phys. Rev. Lett. {\bf 111}, 010401 (2013)]
to obtain the internal energy.
After obtaining the energy eigenstates using the Lanczos diagonalization method,
dynamical quantities are computed via a continued fraction expansion,
a standard procedure for Lanczos-based numerical methods.
Using one-dimensional antiferromagnetic Heisenberg chains with $S=1/2$,
we demonstrate that the proposed procedure is reasonably accurate even for relatively small systems.
